Find the product of (x + (3+5i))^2
2 answers:
Answer:
x^2 +6x +10xi -16 +30i
Step-by-step explanation:
(x + (3+5i))^2
Rewriting as
(x + (3+5i)) (x + (3+5i))
Let 3+5i = m
(x + m) (x + m)
FOILing
x^2 + xm+xm+m^2
x^2 +2xm + m^2
Replacing m with 3+5i
x^2 +2x (3+5i) +(3+5i)^2
Distribute
x^2 +6x +10xi +(3+5i)^2
Now FOIL (3+5i)^2
( 3+5i) ( 3+5i)
3*3+ 3*5i + 3*5i+ 25i^2
= 9 +15i+15i +25(-1)
9+30i -25
-16 +30 i
Replacing that in the equation
x^2 +6x +10xi -16 +30i
Answer:
x² + 6x + 10xi -16 + 30i
Step-by-step explanation:
(x + (3 + 5i) )²
use the binomial theorem:
(a + b)² = a² + 2ab + b² to expand (x + (3 + 5i) )²
substitute the values,
x² + (6 + 10i)x + (-16 + 30i)
therefore
x² + 6x + 10xi -16 + 30i
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